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Note_04M.11-16

Note_04M.11-16 - 11 Insurance Premium The case considered...

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11 Insurance Premium The case considered above involves a potential loss as well as a potential gain. The case of insurance, on the other hand, involves only a potential loss. Let the current value of your property be . You face a chance to incur a loss of L with probability p . If you don’t have an insurance, your property value will be and the expected utility is How much are you willing to pay to insure against the potential loss? If you pay the insurance premium b , your wealth is with certainty. The maximum premium that you are willing to pay is determined by . Another way to look at this is to consider the certainty equivalent C of this risk: and the insurance premium is . This is illustrated below. Example. (see Excel file “utility-insurance”)

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12 Absolute Risk and Relative Risk Examples we have used so far involve a fixed size of risk. Potential gain and loss ( h ) in the example of risk premium and a potential loss ( L ) in the example of insurance premium are fixed amount. These are called the absolute risk . In some cases, the amount of gain or loss may be proportional to the value of the subject. The amount of loss in the example of insurance may depend on the value of the property instead of a fixed amount, that is, . This type of risk is called a relative risk or proportional risk. The risk premium for a relative risk can be defined in the same way as the risk premium of absolute risk. The relative risk in the example of cash vs stock is defined as where " is the fraction of at risk. The relative risk premium ( ) is the fraction of such that is the cash value of W . That is, Recall that the absolute risk premium is defined as B which satisfies
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